CAT 2023 Slot 2 — DILR Question 19

Mixed PracticeEasy

Passage / Data

Answer the following questions based on the information given below:

There are nine boxes arranged in a 3×3 array as shown in Tables 1 and 2. Each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive.

The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of coins in each column is also the same.

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Table 1 gives information regarding the median of the numbers of coins in the three sacks in a box for some of the boxes. In Table 2 each box has a number which represents the number of sacks in that box having more than 5 coins. That number is followed by a * if the sacks in that box satisfy exactly one among the following three conditions, and it is followed by ** if two or more of these conditions are satisfied.

The minimum among the numbers of coins in the three sacks in the box is 1.
The median of the numbers of coins in the three sacks is 1.
The maximum among the numbers of coins in the three sacks in the box is 9.

How many sacks have exactly one coin?

Answer & solution

Answer: 9

Solution

Easy

Same solved grid. Count how many sacks (not boxes) hold exactly one coin — so a box like $(1,1,1)$ contributes three.

The solved grid (each box = three sacks, ascending):

	Col 1	Col 2	Col 3
Row 1	1, 1, 7	3, 9, 9	1, 6, 8
Row 2	1, 2, 9	1, 2, 3	9, 9, 9
Row 3	7, 8, 9	1, 8, 9	1, 1, 1

Tally the $1$ -coin sacks box by box:

\begin{aligned} &\text{C1R1}(1,1,7)\to 2,\quad \text{C1R2}(1,2,9)\to 1,\quad \text{C3R1}(1,6,8)\to 1\\ &\text{C2R2}(1,2,3)\to 1,\quad \text{C2R3}(1,8,9)\to 1,\quad \text{C3R3}(1,1,1)\to 3 \end{aligned}

2+1+1+1+1+3=9

\mathbf{9}\ \text{sacks}